Heretofore workpieces have been positioned on machine base structures such that any movement of the base structure is accommodated in movement of the workpiece. Conventionally it has been necessary to construct base structures using heavyweight material such as granite, i.e. material which remains as stable as possible with variations in temperature and, in order to accommodate as far as possible movement in the fixture on which the base structure is located, the latter is conventionally supported on the fixture with minimum restraints. If lightweight base structures can be utilised it may be that workpieces need not be located on the base structure but directly on the fixture, this possibly leading to relative movement between the base structure and the workpiece resulting in loss of accuracy.